Numerous financial and negotiable instruments exist to facilitate the exchange of goods and services. Others have been created to minimize or exchange risks inherent in underlying transactions. Many have been standardized and trade on regulated exchanges. For example, a promissory note promises the payment of money over a term and is typically employed to facilitate the acquisition of goods. If terms are standardized, then futures and options could be created to assist in transferring the risk in this and similar transactions. By definition, “instruments” provide “formal expression to a legal act or agreement, for the purpose of creating, securing, modifying or terminating a right.” See Black's Law Dictionary, West, Revised 4th Edition, 1968.
Once an instrument is created, it can be purchased and sold. Since instruments have a term, one can bargain in the price. The instrument itself can be purchased and sold over time, and one can “observe” a price at any given point in time (if the instrument is standardized and is listed on a regulated or non-regulated exchange). The fluctuations between observations can be measured with a statistical standard deviation formula known as “volatility.” The instrument itself can be called an “underlying,” when there are instruments that derive their value from it. Volatility is an absolute value, since it is the amount of change, rather than the upward or downward direction of that change.
Volatility between observations can be determined after the observations have occurred. Such historical viewing can provide the data necessary for a calculation of historical volatility. Conceptually, the risks associated with future volatility can be the subject of a bargain, themselves being purchased and sold, and thereby assisting the assumption or minimization of risk. However, prior to the invention herein, there has been no effective standardized mechanism by which a tradable instrument captures the future (realized) volatility of an underlying, in which the instrument has a term, observations during that term, an annualized figure, and wherein final settlement of such an instrument can coincide with the settlement of the options on the underlying.
Risk is a key element in every business and financial decision, and its presence, dictated by the unknown that the future might bring, has been the basis by which the financial markets have prospered. Participants in these markets have been able to reduce or increase their risk by trading instruments that capture price changes in existing markets for such trading. However, participants have heretofore been unable to obtain exposure to changes in the level of that risk by way of standardized instruments.
Contrary to the assumption of popular option-pricing models, changes in market risks can be dramatic. The Bank of International Settlements estimates that $13 trillion of notional over-the-counter (“OTC”) option contracts were outstanding as of June 1999—a twenty times increase from six and one-half years ago. While investment banks seek to delta-hedge this exposure, which effectively neutralizes the directional risk (i.e., whether the contract is trading at a higher or lower price), this still leaves behind significant volatility exposure (that is the amount and speed of change). The same concept holds true for option market makers.
Multi-national corporations, looking closely, may find that in addition to directional risk they really have large amounts of volatility risk. Hedge fund managers and commodity trading advisors could easily use a new asset class to base new, uncorrelated trading programs. And, exchanges are always looking for new products that could enhance volume.
Formulas for calculating volatility, and mechanisms for swapping or minimizing volatility have been considered. For example, Brenner, M. and Dan Galai (1989), “New Financial Instruments for Hedging Changes in Volatility,” Financial Analysts Journal (July-August), pp. 61-65, proposes a so-called “Sigma Index.” Yet, this reference fails to indicate the mechanism for constructing such an index other than by stating that “[i]t could be based on the standard deviation obtained by historical observations (with more weight given to recent observations). It could be based on implied volatilities of options that have just traded. Or we could use a combination of historical and implied volatilities to provide some balance between long and short-run trends.” In no manner, does this reference suggest an instrument, nor a means for trading on the basis of realized volatility over a fixed time period.
Likewise, Whaley, R. E. (1993), “Derivatives on Market Volatility: Hedging Tools Long Overdue,” Journal of Derivatives (Fall) shows a way that the CBOE could trade options on volatility on the S&P 100. The result of this research was the creation of a so-called “Volatility Index (VIX).” Yet, this index is based upon implied volatility. Implied volatility is derived from an options pricing model using the currently traded option premium to infer (or imply) the market's expectation of the future volatility. Since 1993, while being continuously calculated and quoted, no contracts or instruments have been created or traded on this index.
Neuberger, A. (1994), “The Log Contract,” Journal of Portfolio Management (Winter), pp. 74-80, actually teaches away from the instant invention by mentioning (without more) a volatility-type contract, and then dismissing the concept entirely as “inflexible” and “easily manipulated.” Instead, this reference proposes trading the Log Contract, which is merely a futures contract based upon calculating the log of the futures price.
Other indices have emerged that further demonstrate a need for the instant invention. The German Futures & Options Exchange (DTB), presented a volatility index similar to the VIX, called the VDAX which is calculated from the implied volatilities of the options on the DAX index. The VDAX began trading on Dec. 5, 1994.
Also, in 1995, The Austrian Futures and Options Exchange (OTOB) announced a volatility index on its Austrian Traded Index (ATX) for calls and puts. In or about 1995, over-the-counter volatility swaps began trading. In November 1996, Volx became the first volatility futures, but it was based on the implied and historical volatility of three European stock indices: FTSE 100, DAX, and Sweden's OMX. In January 1998, Volax, another volatility futures began trading on the 3-month implied volatility of the DAX. None of these attempts at trading volatility have been successful, and they together demonstrate the long felt need in the industry, and huge potential, for a standardized volatility instrument.
In terms of volatility instruments, although the concept of a contract on historical volatility was mentioned in Brenner and Galai [1989] and actual volatility again in Neuberger [1994], no one has heretofore traveled the path of determining and designing an exchange-tradable contract based upon realized volatility. Rather, it would appear that the academic community has focused on implied volatility and will not consider any alternative.
Concepts and theories for derivatives on implied volatility have a pedigree and basis in mathematics and options theory. However, these indices appear useless as a trading vehicle. According to Brenner, M. and Dan Galai (1997), “Options on Volatility,” Option-Embedded Bonds, Irwin Publishing, Chapter 13, “[w]hile the concept of interpolating a standardized 30-day, at-the-money option from traded options is simple, the implementation can be quite complicated.” Although it is feasible to trade on implied volatility, it is unlikely that such trading would have any serious following. Indeed, no analysis has been performed to determine whether trading on implied volatility would even appeal to market participants, or what they would find useful. For a contract to be successful, it has to be understandable by more than just a few of the most sophisticated players. Unfortunately, few traders will understand all of the math, option theory, averaging, adjustments for weekends, rolling, interpolation, extrapolation, limitations, and assumptions possessed by a contract on implied volatility.
Even if an army of educators descended upon the globe to make sure everyone understood completely the concept of trading on implied volatility, there would nonetheless remain a number of problems.